1. Approximation of the Hilbert Transform on the unit circle
- Author
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Fermo, Luisa and Loi, Valerio
- Subjects
Mathematics - Numerical Analysis ,65D30, 42A10, 30E20, 32A55 - Abstract
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szeg\"o and anti-Szeg\"o quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy through their averaged results. Their computation involves a free parameter associated with the corresponding para-orthogonal polynomials. Here, it is suitably chosen to construct a Szeg\"o and anti-Szeg\"o formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.
- Published
- 2024